6x-2x(x-4)=3x+5

Solution for 6x-2x(x-4)=3x+5 equation:

6x-2x(x-4)=3x+5

We move all terms to the left:

6x-2x(x-4)-(3x+5)=0

We multiply parentheses

-2x^2+6x+8x-(3x+5)=0

We get rid of parentheses

-2x^2+6x+8x-3x-5=0

We add all the numbers together, and all the variables

-2x^2+11x-5=0

a = -2; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-2)·(-5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*-2}=\frac{-2}{-4}
=1/2
$